Stationarity of Regression Relationships: Application to Empirical Downscaling

Abstract

The performance of a statistical downscaling model is usually evaluated for its ability to explain a large fraction of predictand variance. In this note, it is shown that although this fraction may be high, the longest time scales, including trends, may not be explained by the model. This implies that the model is nonstationary over the training period of the model, and it questions the basic stationarity assumption of statistical downscaling. This is exemplified by using a simple regression model for downscaling European precipitation and surface temperature where appropriate Monte Carlo?based field significance tests are developed, taking into account the intercorrelation between predictand series. Based on this test, it is concluded that care is needed in selecting predictors to avoid this form of nonstationarity. Even though this is illustrated for a simple regression-type statistical downscaling model, the main conclusions may also be valid for more complicated models.